Linear Sampling Method For A Class Of Inverse Obstacle Scattering Problems

This paper focuses on the scattering of a mixture of penetrable obstacles and non-penetrable obstacles in the R² space.Given appropriate boundary conditions,the mixed boundary value problem we consider can be summarized as follows:find the solution ??H_loc¹?R²\????1??????2??and ?? H¹??₁?satisfying the following questions:We use ?¹???R² to denote the obstacle that can be penetrated and ?_C???R² the obstacle that cannot be penetrated.The two obstacles do not intersect with each other.Otherwise,v to denote the unit outside normal of ?₁ and ?₂.Where h₁?H^-1/2?????₁?,h₂?H^-1/2?????₁?and h₃?H^1/2?????₂?,k₀>0 and k₁>0 are wave numbers,??0 is a parameter.The ultimate goal of this paper is to study the inverse scattering problem of the problem above,which is to reconstruct the shape of the obstacles ?₁ and ?₂ through far-field information.The inverse problem is related to the positive problem,because of this,we mainly study the well-posedness of the solution to the problem above,that is,the existence and uniqueness of the solution.The ex:istence is proved by using boundary integral equation.The uniqueness is based on the basic tools of Rellich's lemma and Green formula.The corresponding inverse scattering problem is studied by sampling method.